1. Results by Network

Table OA1. Expected percentage point change in the probability of a given action chain reaching the last mile (Model 1) and developing into the best idea (Model 2) corresponding to one additional change activity, by Social Network and ss-max.

Actor chooses max performing idea
(ss-max = TRUE)

Actor chooses better performing idea
(ss-max = FALSE)

Small World I

Small World II

Small World III

Random

Fully-Connected

Small World I

Small World II

Small World III

Random

Fully-Connected

Model 1

Model 2

Model 1

Model 2

Model 1

Model 2

Model 1

Model 2

Model 1

Model 2

Model 1

Model 2

Model 1

Model 2

Model 1

Model 2

Model 1

Model 2

Model 1

Model 2

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Action chain activity

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

(13)

(14)

(15)

(16)

(17)

(18)

(19)

(20)

Within-network-community recombination

1.97

-8.00

1.79

-8.51

1.83

-6.95

0.58

-2.60

0.78

-2.85

0.61

-2.74

Between-network-community recombination

3.43

-6.10

2.29

-5.98

2.25

-5.04

1.79

-1.23

1.10

-1.66

0.98

-1.96

Within-network-community transfer

-0.61

-0.40ns

-0.69

0.62

-0.50

0.08

-0.55

0.19

-0.39

0.85

-0.30

0.85

Between-network-community transfer

0.73

4.63

0.47ns

4.68

-0.12

4.10

0.64

5.19

-0.15

3.63

-0.11

3.00

Self-search

-1.18

17.01

-1.09

17.05

-1.16

16.76

-0.83

16.85

-0.76

15.84

-0.25

8.00

-0.37

7.36

-0.25

7.13

-0.25

7.81

-0.18

6.93

Recombination

1.52

-6.21

0.96

-4.45

0.67

-2.06

0.36

-1.48

Transfer

-0.31

2.23

-0.11

1.79

-0.15

0.94

-0.03

1.14

No. of observations (chains)

36,905

16,921

37,029

17,273

36,956

17,515

37,127

17,203

37,184

18,968

37,007

20,147

37,111

20,309

36,989

20,782

36,995

20,295

37,075

22,059

Notes:

nsEstimated coefficients are not statistically significant at the 95% confidence level

Probability changes calculated for the median observation using logistic regressions. Model 1 estimates are based on logistic estimation of a binary outcome: 1 if the action chain was the first in a given model run to reach last mile and 0 if otherwise. Model 2 estimates are based on logistic estimation of a binary outcome: 1 if the action chain was the first in a given model run to reach the best possible discoverable idea and 0 if otherwise.

Recombinations and transfers cannot be disaggregated by between- and within-network community in random and fully-connected networks because these network structures do not have network communities.

Estimations made using data from 50,000 runs for each network and ss-max condition (5,000 runs by lanscape). All runs used parameters collab = 0.8 and recomb = 0.8.




2. Results by Landscape

Table OA2. Expected percentage point change in the probability of a given action chain reaching the last mile (Model 1) and developing into the best idea (Model 2) corresponding to one additional change activity, by Landscape and ss-max.


Actor chooses max performing idea
(ss-max = TRUE)

Custom landscape

N=8, K=2

N=8, K=4

N=8, K=6

N=10, K=2

N=10, K=4

N=10, K=6

N=12, K=2

N=12, K=4

N=12, K=6

Model 1

Model 2

Model 1

Model 2

Model 1

Model 2

Model 1

Model 2

Model 1

Model 2

Model 1

Model 2

Model 1

Model 2

Model 1

Model 2

Model 1

Model 2

Model 1

Model 2

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Action chain activity

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

(13)

(14)

(15)

(16)

(17)

(18)

(19)

(20)

Within-network-community recombination

1.14

-6.39

2.88

-5.25

3.91

-9.85

3.35

-9.23

2.02

-6.32

2.30

-8.44

2.18

-8.68

1.44

-4.71

1.70

-6.33

1.47

-10.14

Between-network-community recombination

2.49

-2.72

3.35

-5.88

4.37

-4.44

3.14

-10.99

2.73

-5.50

2.93

-5.73

2.15

-9.51

2.90

-2.94

2.60

-3.95

2.03

-6.41

Within-network-community transfer

-0.45

0.39ns

-1.09

1.35

-0.72

1.53

-0.74

-1.55

-0.73

0.62

-0.73

0.23

-0.54

0.46

-0.58

-1.02

-0.46

-1.00

-0.47

-0.64

Between-network-community transfer

0.92

3.05

-0.08ns

3.94

-1.10

0.94

-0.62

1.13

0.45

4.63

0.12

3.39

0.11

1.40

0.63

3.69

0.55

5.04

0.36

0.22

Self-search

-1.06

8.03

-1.79

14.81

-2.29

30.79

-1.93

22.28

-1.53

19.48

-1.53

19.48

-1.29

26.10

-1.29

14.97

-1.26

16.92

-0.90

19.98

No. of observations (chains)

21,741

6,324

12,677

13,922

17,793

9,155

21,577

4,832

13,763

13,449

18,890

8,515

21,996

4,652

14,718

13,066

19,677

8,149

22,645

4,024

Actor chooses better performing idea
(ss-max = FALSE)

Custom landscape

N=8, K=2

N=8, K=4

N=8, K=6

N=10, K=2

N=10, K=4

N=10, K=6

N=12, K=2

N=12, K=4

N=12, K=6

Model 1

Model 2

Model 1

Model 2

Model 1

Model 2

Model 1

Model 2

Model 1

Model 2

Model 1

Model 2

Model 1

Model 2

Model 1

Model 2

Model 1

Model 2

Model 1

Model 2

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Action chain activity

(21)

(22)

(23)

(24)

(25)

(26)

(27)

(28)

(29)

(30)

(31)

(32)

(33)

(34)

(35)

(36)

(37)

(38)

(39)

(40)

Within-network-community recombination

0.77

-3.28

0.55

-3.03

1.33

-3.86

1.36

-5.44

0.13ns

-1.59

0.37

-1.75

0.77

-1.62

0.21ns

-1.30

0.35

-1.97

0.69

-1.97

Between-network-community recombination

2.64

-1.52

0.51ns

-1.74

0.94

-1.86

1.44

-0.59ns

0.47

-1.81

0.97

-0.92ns

1.11

-1.24ns

0.77

-1.37

0.86

-0.51ns

1.14

-1.70

Within-network-community transfer

-0.35

0.53ns

-0.95

1.10

-1.01

1.02ns

-0.79

0.74ns

-0.38

0.19ns

-0.33

-0.22ns

-0.76

0.45ns

-0.45

0.70

-0.28

0.05ns

-0.37

0.99ns

Between-network-community transfer

0.96

6.24

-0.28ns

3.65

-0.94

2.07ns

0.07ns

0.63ns

0.57ns

2.34

-0.11ns

1.85ns

-0.08ns

0.60ns

0.05ns

2.80

-0.41ns

3.41

-0.07ns

1.64ns

Self-search

-0.84

4.74

-0.11ns

11.96

-0.19ns

12.24

-0.39

14.37

-0.21

8.14

-0.14ns

8.24

-0.21

8.82

-0.22

5.43

-0.19

6.91

-0.30

6.70

No. of observations (chains)

21,581

7,319

12,782

15,202

17,939

10,482

21,597

5,826

13,680

15,283

18,763

10,582

22,074

6,001

14,595

15,191

19,670

10,424

22,597

5,810

Notes:

nsEstimated coefficients are not statistically significant at the 95% confidence level

Probability changes calculated for the median observation using logistic regressions. Model 1 estimates are based on logistic estimation of a binary outcome: 1 if the action chain was the first in a given model run to reach last mile and 0 if otherwise. Model 2 estimates are based on logistic estimation of a binary outcome: 1 if the action chain was the first in a given model run to reach the best possible discoverable idea and 0 if otherwise.

Estimations made using data from 25,000 runs for each landscape and ss-max condition. All runs used Small World II network, and parameters collab = 0.8 and recomb = 0.8.




3. Results by Environment

Table OA3. Expected percentage point change in the probability of a given action chain reaching the last mile (Model 1) and developing into the best idea (Model 2) corresponding to one additional change activity, by Environment and ss-max.

Actor chooses max performing idea
(ss-max = TRUE)

Actor chooses better performing idea
(ss-max = FALSE)

collab = 0.3 & recomb = 0.3

collab = 0.3 & recomb = 0.8

collab = 0.8 & recomb = 0.3

collab = 0.8 & recomb = 0.8

collab = 0.3 & recomb = 0.3

collab = 0.3 & recomb = 0.8

collab = 0.8 & recomb = 0.3

collab = 0.8 & recomb = 0.8

Model 1

Model 2

Model 1

Model 2

Model 1

Model 2

Model 1

Model 2

Model 1

Model 2

Model 1

Model 2

Model 1

Model 2

Model 1

Model 2

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Action chain activity

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

(13)

(14)

(15)

(16)

Within-network-community recombination

9.23

-6.58

4.08

-7.78

2.96

-11.71

1.94

-7.92

2.26

-11.17

1.98

-11.76

2.14

-4.35

0.61

-2.69

Between-network-community recombination

10.81

-5.14

3.98

-7.26

3.19

-12.49

2.66

-5.66

3.91

-9.07

2.02

-10.31

2.89

-5.70

1.10

-1.79

Within-network-community transfer

-0.01

1.55ns

-0.13

0.43

-0.07

1.84

-0.58

-0.03

-0.82

-1.16

-0.64

0.73

-0.25

-0.24

-0.41

0.56

Between-network-community transfer

-0.01

1.66

-0.12ns

0.90

0.07

6.68

0.21

3.53

-0.61

-0.28

-0.65

-0.79

0.01

3.05

-0.01

3.36

Self-search

-0.01

1.90

-0.19

1.19

-0.09

28.71

-1.21

16.77

-0.07

11.23

-0.27

11.07

0.23

9.78

-0.26

7.39

No. of observations (chains)

185,403

65,046

185,402

67,388

185,348

67,660

185,477

86,088

185,547

78,926

185,394

82,304

184,846

77,057

185,278

102,120

Notes:

nsEstimated coefficients are not statistically significant at the 95% confidence level

Probability changes calculated for the median observation using logistic regressions. Model 1 estimates are based on logistic estimation of a binary outcome: 1 if the action chain was the first in a given model run to reach last mile and 0 if otherwise. Model 2 estimates are based on logistic estimation of a binary outcome: 1 if the action chain was the first in a given model run to reach the best possible discoverable idea and 0 if otherwise.

Estimations made using data from 250,000 runs for each environment and ss-max condition (25,000 runs by landscape). All runs used network Small World II.




4. Results by Partner Selection Process

Table OA4. Expected percentage point change in the probability of a given action chain reaching the last mile (Model 1) and developing into the best idea (Model 2) corresponding to one additional change activity, by partner selection process.

Random partner selection

Performance based partner selection

Model 1

Model 2

Model 1

Model 2

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Action chain acivity

(1)

(2)

(3)

(4)

Within-network-community recombination

1.79

-8.51

2.16

-9.70

Between-network-community recombination

2.29

-5.98

2.69

-5.96

Within-network-community transfer

-0.69

0.62ns

-0.54

-0.48

Between-network-community transfer

0.47

4.68

0.06ns

6.66

Self-search

-1.09

17.05

-0.96

17.72

No. of observations (chains)

37,029

17,273

37,002

16,513

Notes:

nsEstimated coefficients are not statistically significant at the 95% confidence level.

'Performance based partner selection' results are based on a version of the model where ego only interacts with alters who are better performing. 'Random partner selection' results are equivalent to those presented in table 2 of the main paper, provided here for comparison purposes.

Probability changes calculated for the median observation using logistic regressions. Model 1 estimates are based on logistic estimation of a binary outcome: 1 if the action chain was the first in a given model run to reach last mile and 0 if otherwise. Model 2 estimates are based on logistic estimation of a binary outcome: 1 if the action chain was the first in a given model run to reach the best possible discoverable idea and 0 if otherwise.

Estimations made using data from 50,000 runs for each Model version (5,000 runs by lanscape). All runs used Small World II network, and parameters collab = 0.8, recomb = 0.8 and ss-max = TRUE.

5. Results by Initial Condition

Table OA5. Expected percentage point change in the probability of a given action chain reaching the last mile (Model 1) and developing into the best idea (Model 2) corresponding to one additional change activity, by initial condition.

Actors starting outside the global basin

Actors starting at any location

Model 1

Model 2

Model 1

Model 2

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Action chain acivity

(1)

(2)

(3)

(4)

Within-network-community recombination

1.79

-8.51

1.44

-6.00

Between-network-community recombination

2.29

-5.98

2.10

-3.51

Within-network-community transfer

-0.69

0.62ns

-0.40

-1.20

Between-network-community transfer

0.47

4.68

0.32ns

3.99

Self-search

-1.09

17.05

-0.89

16.96

No. of observations (chains)

37,029

17,273

36,596

17,769

Notes:

nsEstimated coefficients are not statistically significant at the 95% confidence level.

'Actors starting outside the global basin' results are equivalent to those presented in table 2 of the main paper, provided here for comparison purposes. In said model, the centroid for the network community could not be a location from which an actor could find the global peak through only self-search. 'Actors starting at any location' results are based on a version of the model that relaxes that restriction.

Probability changes calculated for the median observation using logistic regressions. Model 1 estimates are based on logistic estimation of a binary outcome: 1 if the action chain was the first in a given model run to reach last mile and 0 if otherwise. Model 2 estimates are based on logistic estimation of a binary outcome: 1 if the action chain was the first in a given model run to reach the best possible discoverable idea and 0 if otherwise.

Estimations made using data from 50,000 runs for each Model version (5,000 runs by lanscape). All runs used Small World II network, and parameters collab = 0.8, recomb = 0.8 and ss-max = TRUE.